LinearControl

SystemsSystems

Basic Information

• Instructor Contact Information

– moosavi@profs.hut.ac.ir– moosavi@profs.hut.ac.ir

– Phone : 8411-506

Class Webpage• http://profs.hut.ac.ir/~moosavi/control

• Please check the page for– Any announcement– HW assignments– HW assignments– Grades– Any additional material

Final Grade Weighting Schedule

• Homework average: 10%• Quizzes: 10%• Midterm exam: 30%• Final exam: 50%• Final exam: 50%• Bonus: 0-5%

Student behavior expectations

• Full attendance expected, except with prior-notified excuses

• On-time arrival• Be active • Be considerate to students and TA• Help each other in reviewing notes, HW, Matlab

Accommodation/Assistance• Please let me know if you

– Have any medical/mental/emergency conditions– Have special requests– Want me to adjust lecture contents/pace

• Can also consult me if you – Would like to seek advice on any professional or

personal issues

Course Description• Linear Control Systems. (3 credit) • Prereq: Signals & Systems• Stability and performance analysis of

automatic control systems. The root locus,and frequency response methods forand frequency response methods forcontrol systems design. PID control andlead-lag compensation. Computer tools forcontrol system analysis and design.

Prerequisite by topics• Concept and solution of linear ordinary

differential equations• Laplace transform and its applications• Poles, zeros, transfer functions, frequency

response, Bode plotsresponse, Bode plots• Vectors and matrices• Complex numbers• Knowledge and proficiency in Matlab

OBJECTIVES• On completion of this course, the student will be able to do the following either by

hand or with the help of computation tools such as Matlab: – Define the basic terminologies used in controls systems– Explain advantages and drawbacks of open-loop and closed loop control systems– Obtain models of simple dynamic systems in ordinary differential equation, transfer function,

state space, or block diagram form– Obtain overall transfer function of a system using either block diagram algebra, or signal flow

graphs, or Matlab tools.– Compute and present in graphical form the output response of control systems to typical test

input signalsinput signals– Explain the relationship between system output response and transfer function

characteristics or pole/zero locations– Determine the stability of a closed-loop control systems using the Routh-Hurwitz criteria– Analyze the closed loop stability and performance of control systems based on open-loop

transfer functions using the Root Locus technique– Design PID or lead-lag compensator to improve the closed loop system stability and

performance using the Root Locus technique– Analyze the closed loop stability and performance of control systems based on open-loop

transfer functions using the frequency response techniques– Design PID or lead-lag compensator to improve the closed loop system stability and

performance using the frequency response techniques

Topics Covered• Review of signal systems concepts and techniques applied to

control system• Block diagrams and signal flow graphs• Modeling of control systems using ode, block diagrams, and transfer

functions• Modeling and analysis of control systems using state space

methods• Analysis of dynamic response of control systems, including transient • Analysis of dynamic response of control systems, including transient

response, steady state response, and tracking performance.• Closed-loop stability analysis using the Routh-Hurwitz criteria• Stability and performance analysis using the Root Locus techniques• Control system design using the Root Locus techniques• Stability and performance analysis using the frequency response

techniques• Control system design using the frequency response techniques

Textbook• Modern Control Systems (11th Edition) by

Richard C. Dorf and Robert H. Bishop

Other References• Modern Control Engineering (5th Edition) by Katsuhiko

Ogata

Other References

• Automatic Control Systems, Golnaraghi and Kuo, ninth edition, Wiley, 2009

collaboration and helping each other

• For tasks not intended for group work, individualsubmission is required. In this case, you are encouragedto discuss among your friends on how to attack problems.However, you should write your own solution.

• Copying other people’s work is strictly prohibited.

Academic dishonesty

• Cheating is a very serious offense. It will be dealt with in the most severe manner allowable under University regulations. If caught cheating, you can expect a failing grade and initiation of a cheating case in the University grade and initiation of a cheating case in the University system.

Control System Terminology

• Input - Excitation applied to a control system from an external source.

• Output - The response obtained from a system

• Feedback - The output of a system that is returned to modify the input.

• Error - The difference between the reference input and the output.

Negative Feedback Control System

CONTROLLERCONTROLLED DEVICE

+ ++

DEVICE

FEEDBACK ELEMENT

-

Types of Control Systems�Open-Loop

– Simple control system which performs its function with-out concerns for initial conditions or external inputs.

– Must be closely monitored.

�Closed-Loop (feedback)�Closed-Loop (feedback)– Uses the output of the process to modify the

process to produce the desired result.– Continually adjusts the process.

Advantages of a Closed-Loop Feedback System

� Increased Accuracy– Increased ability to reproduce output with varied

input.�Reduced Sensitivity to Disturbance

– By self correcting it minimizes effects of system – By self correcting it minimizes effects of system changes.

�Smoothing and Filtering– System induced noise and distortion are reduced.

� Increased Bandwidth– Produces satisfactory response to increased range

of input changes.

Major Types of Feedback Used�Position Feedback

– Used when the output is a linear distance or angular measurement.

�Rate & Acceleration Feedback– Feeds back rate of motion or rate of change – Feeds back rate of motion or rate of change

of motion (acceleration)– Motion smoothing– Uses an electrical/mechanical device called

an accelerometer

PresentPosition

FuturePosition

Fire Control Problem

Ship’s Heading Range Change

BearingChange

Fire Control Problem

• Input– Target data– Own ship data

• Computations– Relative motion procedure– Relative motion procedure– Exterior ballistics procedure

Fire Control Problem• Solutions

– Weapons time of flight– Bearing rate– Line of Sight(LOS): The line between the target and the

firing platform– Speed across LOS– Future target position– Future target position– Launch angles

• Launch azimuth• Launch elevation

– Weapon positioning orders• The above determines weapon trajectory: The line the weapon

must travel on to intercept the target.

The Iterative Process to the Fire Control Solution

Step 1

Step 2

Step 3 Last Step

A 3-Dimensional Problem

Line of Sight

Horizontal Reference Plane

TargetElevation

GunElevation

Solving the Fire Control Problem

Continuously MeasurePresent Target Position

Stabilize MeasuredQuantities

Compute RelativeTarget Velocity

Environmental Inputs

BallisticCalculations

Relative Motion

Calculations

Time ofFlight

Future TargetPosition

Prediction Procedure

UnstabilizedLaunchAngles

Environmental Inputs

Launch Angles(Stabilized)

Weapons Positioning orders

Idle-speed control system.

Solar collector field Conceptual method of efficient water extraction using solar power.

Important components of the sun-tracking control system.

a. system concept;b. detailed layout;c. schematic;d. functional block diagram

Antenna azimuth position control system:

Computer hard disk drive,

showing disks showing disks and read/write

head

Courtesy of Quantum Corp.

Response of a position control system showing

effect of high

High gain; fast but oscillating

effect of high and low

controller gain on the output

responseControl goal; fast reaction, lower overshoot, less settling time

The control system design processAircraft attitude defined